Statistical inference for continuous-time locally stationary processes using stationary approximations

05/10/2021 ∙ by Bennet Ströh, et al. ∙ 0

We establish asymptotic properties of M-estimators, defined in terms of a contrast function and observations from a continuous-time locally stationary process. Using the stationary approximation of the sequence, θ-weak dependence, and hereditary properties, we give sufficient conditions on the contrast function that ensure consistency and asymptotic normality of the M-estimator. As an example, we obtain consistency and asymptotic normality of a localized least squares estimator for observations from a sequence of time-varying Lévy-driven Ornstein-Uhlenbeck processes. Furthermore, for a sequence of time-varying Lévy-driven state space models, we show consistency of a localized Whittle estimator and an M-estimator that is based on a quasi maximum likelihood contrast. Simulation studies show the applicability of the estimation procedures.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.